Ion-mediated nucleic acid helix-helix interactions

Salt ions are essential for the folding of nucleic acids. We use the tightly bound ion (TBI) model, which can account for the correlations and fluctuations for the ions bound to the nucleic acids, to investigate the electrostatic free-energy landscape for two parallel nucleic acid helices in the solution of added salt. The theory is based on realistic atomic structures of the helices. In monovalent salt, the helices are predicted to repel each other. For divalent salt, while the mean-field Poisson-Boltzmann theory predicts only the repulsion, the TBI theory predicts an effective attraction between the helices. The helices are predicted to be stabilized at an interhelix distance approximately 26-36 A, and the strength of the attractive force can reach -0.37 k(B)T/bp for helix length in the range of 9-12 bp. Both the stable helix-helix distance and the strength of the attraction are strongly dependent on the salt concentration and ion size. With the increase of the salt concentration, the helix-helix attraction becomes stronger and the most stable helix-helix separation distance becomes smaller. For divalent ions, at very high ion concentration, further addition of ions leads to the weakening of the attraction. Smaller ion size causes stronger helix-helix attraction and stabilizes the helices at a shorter distance. In addition, the TBI model shows that a decrease in the solvent dielectric constant would enhance the ion-mediated attraction. The theoretical findings from the TBI theory agree with the experimental measurements on the osmotic pressure of DNA array as well as the results from the computer simulations.     

FtsZ bacterial cytoskeletal polymers on curved surfaces: the importance of lateral interactions

A recent theoretical article provided a mechanical explanation for the formation of cytoskeletal rings and helices in bacteria assuming that these shapes arise, at least in part, from the interaction of the inherent mechanical properties of the protein polymers and the constraints imposed by the curved cell membrane (Andrews, S., and A. P. Arkin. 2007. Biophys. J. 93:1872-1884). Due to the lack of experimental data regarding the bending rigidity and preferential bond angles of bacterial polymers, the authors explored their model over wide ranges of preferred curvature values. In this letter, we present the shape diagram of the FtsZ bacterial polymer on a curved surface but now including recent experimental data on the in vitro formed FtsZ polymers. The lateral interactions between filaments observed experimentally change qualitatively the shape diagram and indicate that the formation of rings over spirals is more energetically favored than estimated in the above-mentioned article.     

A minimal kinetic model for a viral DNA packaging machine

Terminase enzymes are common to both eukaryotic and prokaryotic double-stranded DNA viruses. These enzymes possess ATPase and nuclease activities that work in concert to "package" a viral genome into an empty procapsid, and it is likely that terminase enzymes from disparate viruses utilize a common packaging mechanism. Bacteriophage lambda terminase possesses a site-specific nuclease activity, a so-called helicase activity, a DNA translocase activity, and multiple ATPase catalytic sites that function to package viral DNA. Allosteric interactions between the multiple catalytic sites have been reported. This study probes these catalytic interactions using enzyme kinetic, photoaffinity labeling, and vanadate inhibition studies. The ensemble of data forms the basis for a minimal kinetic model for lambda terminase. The model incorporates an ADP-driven conformational reorganization of the terminase subunits assembled on viral DNA, which is central to the activation of a catalytically competent packaging machine. The proposed model provides a unifying mechanism for allosteric interaction between the multiple catalytic sites of the holoenzyme and explains much of the kinetic data in the literature. Given that similar packaging mechanisms have been proposed for viruses as dissimilar as lambda and the herpes viruses, the model may find general utility in our global understanding of the enzymology of virus assembly.     

DNA as Membrane-Bound Ligand-Receptor Pairs: Duplex Stability Is Tuned by Intermembrane Forces

We use membrane-anchored DNA as model adhesion receptors between lipid vesicles. By studying the thermal stability of DNA duplex formation, which tethers the vesicles into superstructures, we show that the melting temperature of a 10-base DNA sequence is dependent on the lipid composition of the tethered vesicles. We propose a simple model that describes how the intermembrane interactions tilt the free energy landscape for DNA binding. From our model, we estimate the area per DNA in the binding sites between vesicles and also the total area of the adhesion plaques. We find that vesicles containing a small proportion of cationic lipid that are modified with membrane-anchored DNA can be reversibly tethered by specific DNA interactions and that the DNA also induces a small attraction between these membranes, which stabilizes the DNA duplex. By increasing the equilibrium intermembrane distance on binding, we show that intermembrane interactions become negligible for the binding thermodynamics of the DNA and hence the thermal stability of vesicle aggregates becomes independent of lipid composition at large enough intervesicle separations. We discuss the implications of our findings with regards to cell adhesion and fusion receptors, and the programmable self-assembly of nano-structured materials by DNA hybridization.     

Three-dimensional structure of complexes of single-stranded DNA-binding proteins with DNA. IKe and fd gene 5 proteins form left-handed helices with single-stranded DNA

Specimen-tilting in an electron microscope was used to determine the three-dimensional architecture of the helical complexes formed with DNA by the closely related single-stranded DNA binding proteins of fd and IKe filamentous viruses. The fd gene 5 protein is the only member of the DNA-helix-destabilizing class of proteins whose structure has been determined crystallographically, and yet a parameter essential to molecular modeling of the co-operative interaction of this protein with DNA, the helix handedness, has not been available prior to this work. We find that complexes formed by titrating fd viral DNA with either the fd or IKe gene 5 protein have a left-handed helical sense. Complexes isolated from Escherichia coli infected by fd virus are also found to be left-handed helical; hence, the left-handed fd helices are not an artefact of reconstitution in vitro. Because the proteins and nucleic acid of the complexes are composed of asymmetric units which cannot be fitted equivalently to right-handed and left-handed helices, these results rule out a previous computer graphics atomic model for the helical fd complexes: a right-handed helix had been assumed for the model. Our work provides a defined three-dimensional structural framework within which to model the protein-DNA and protein-protein interactions of two structurally related proteins that bind contiguously and co-operatively on single-stranded DNAs.     

Nucleosome positioning and nucleosome stacking: two faces of the same coin

Nucleosomes are regularly spaced along eukaryotic genomes. In the emerging model, known as "statistical positioning", this spacing is due to steric repulsion between nucleosomes and to the presence of nucleosome excluding barriers on the genome. However, new experimental evidence recently challenged the "statistical positioning" model (Z. Zhang et al., Science, 2011, 332(6032), 977-980). We propose here that the regular spacing can be better explained by adding attractive interactions between nucleosomes. In our model those attractions are due to the fact that nucleosomes are stacked in regular chromatin fibers. In a self-reinforcing mechanism, regular nucleosome spacing promotes in turn nucleosome stacking. We first show that this model can precisely account for the nucleosome spacing observed in Saccharomyces cerevisiae. We then use a simple toy model to show that attraction between nucleosomes can fasten the formation of the chromatin fiber.     

TRANSFORMATION OF NONPOLAR FILAMENTS OF THE BLUE-GREEN ALGA GLOEOTRICHIA ECHINULATA U. WISC. 1052 INTO DOUBLE HELICES12

Normally straight filaments of Gloeotrichia echinulata U. Wisc. 1052 transform into double helices when a critical culture density has been attained. In inorganic Zehnder-Gorham's medium No. 11, the alga initially is morphologically uniform and forms single, lightly curved, polar filaments. When a stage of close proximity of the filaments is reached, excessively long filaments are observed that are nonpolar. Some of these nonpolar filaments form helices. Two independent single helices may entwine to form a double helix. Double helices also form when both ends of an excessively long filament meet and start entwining until a loop is left at about the original middle of the filament. In another manner of double-helix formation, a straight filament makes a hairpin bend at about its middle; then 2 helices form starting at the bend and they entwine into a double helix, leaving a loop at the location of the original bend. Under proper culture conditions, the structures of double helices show an amazing regularity. Once double-helix formation has started, some strong force brings the process to completion. In a mature culture, helices disintegrate into apparently healthy, short pieces of filaments or single cells, while the straight or slightly curved polar filaments still persist. Helical transformation of nonpolar filaments does not appear to be a sign of nutritional or other stress but rather appears to serve a specific purpose. One might speculate that a genetic exchange between opposite cells takes place.     

Spatial resolution of two bacterial cell division proteins: ZapA recruits ZapB to the inner face of the Z‐ring

FtsZ, the essential regulator of bacterial cell division, is a dynamic cytoskeletal protein that forms helices that condense into the Z‐ring prior to division. Two small coiled‐coil proteins, ZapA and ZapB, are both recruited early to the Z‐ring. We show here that ZapB is recruited to the Z‐ring by ZapA. A direct interaction between ZapA and ZapB is supported by bacterial two‐hybrid and in vitro interaction assays. Using high‐resolution 3‐D reconstruction microscopy, we find that, surprisingly, ZapB is located inside the Z‐ring in virtually all cells investigated. We propose a molecular model in which ZapA increases lateral interactions between FtsZ proto‐filaments and ZapB mediates further stabilization of this interaction by cross‐linking ZapA molecules bound to adjacent FtsZ proto‐filaments. Gene deletion and complementation assays show that ZapB can mitigate cell division and Z‐ring assembly defects even in the absence of ZapA, raising the possibility that ZapB stimulates Z‐ring assembly by two different mechanisms.     

The bacterial flagellum as an imperfect cylindrical crystal: flagellar geometry, movement and polymorphism, and the role of partial dislocations

A pairing attraction between helical turns of subunits in a cylindrical crystal, like that in the dahlemense strain of tobacco mosaic virus, can cause the axis of the rod or crystal to become helical. This is true only if the number of helices is odd. The shape of a bacterial flagellum can be accounted for then if, as Caspar &; Holmes and Klug have suggested, rows of its subunits exhibit such a pairing interaction. Klug's thoughts on bacterial flagella are developed and extended into a model that accounts qualitatively for geometry, movement and polymorphism of flagella. If the number of helices between which there is a pairing interaction is odd, then the crystal is an imperfect cylindrical crystal. The geometry of such crystals is described. They contain a line defect, termed here an antiphase boundary, across which the pairing interaction is reversed. The boundary is a line of expansion on the convex side of a curved filament. Movement of flagella is explained by circumferential displacement of the antiphase boundary. One polymorphic form can convert to another if a dislocation passes along it. Straight flagella are perfect cylindrical crystals with no antiphase boundary.     

Nanosurfer assay dissects β-cardiac myosin and cardiac myosin-binding protein C interactions

Cardiac myosin-binding protein C (cMyBP-C) modulates cardiac contractility through putative interactions with the myosin S2 tail and/or the thin filament. The relative contribution of these binding-partner interactions to cMyBP-C modulatory function remains unclear. Hence, we developed a “nanosurfer” assay as a model system to interrogate these cMyBP-C binding-partner interactions. Synthetic thick filaments were generated using recombinant human β-cardiac myosin subfragments (HMM or S1) attached to DNA nanotubes, with 14- or 28-nm spacing, corresponding to the 14.3-nm myosin spacing in native thick filaments. The nanosurfer assay consists of DNA nanotubes added to the in vitro motility assay so that myosins on the motility surface effectively deliver thin filaments to the DNA nanotubes, enhancing thin filament gliding probability on the DNA nanotubes. Thin filament velocities on nanotubes with either 14- or 28-nm myosin spacing were no different. We then characterized the effects of cMyBP-C on thin filament motility by alternating HMM and cMyBP-C N-terminal fragments (C0–C2 or C1–C2) on nanotubes every 14 nm. Both C0–C2 and C1–C2 reduced thin filament velocity four- to sixfold relative to HMM alone. Similar inhibition occurred using the myosin S1 construct, which lacks the myosin S2 region proposed to interact with cMyBP-C, suggesting that the cMyBP-C N terminus must interact with other myosin head domains and/or actin to slow thin filament velocity. Thin filament velocity was unaffected by the C0–C1f fragment, which lacks the majority of the M-domain, supporting the importance of this domain for inhibitory interaction(s). A C0–C2 fragment with phospho-mimetic replacement in the M-domain showed markedly less inhibition of thin filament velocity compared with its phospho-null counterpart, highlighting the modulatory role of M-domain phosphorylation on cMyBP-C function. Therefore, the nanosurfer assay provides a platform to precisely manipulate spatially dependent cMyBP-C binding-partner interactions, shedding light on the molecular regulation of β-cardiac myosin contractility.     

Aromatic and cation-pi interactions enhance helix-helix association in a membrane environment

The cation-pi interaction is an electrostatic attraction between a positive charge and the conjugated pi electrons of an aromatic ring. These interactions are well documented in soluble proteins and can be both structurally and functionally important. Catalyzed by observations in our laboratory that an Ala- and Ile-rich two-helix transmembrane segment tended to form SDS-resistant dimers upon the incorporation of suitably located Trp residues, here we have constructed a library of related constructs to study systematically the impact of aromatic-aromatic and cation-pi interactions on tertiary structure formation within an Escherichia coli membrane. Using the TOXCAT oligomerization assay with the hydrophobic segment AIAIAIIAZAXAIIAIAIAI, where Z = A, W, Y, or F and X = A, H, R, or K in all possible combinations of cation and/or aromatic pairings, to assess the TM-TM dependent expression of the chloramphenicol acetyltransferase reporter gene, we find that cation-pi interactions, particularly between Lys and Trp, Tyr, or Phe, as well as weakly polar interactions between pairs of aromatic residues, significantly enhance the strength of oligomerization of these hydrophobic helices, in some instances forming oligomers four times stronger than the high-affinity glycophorin A dimer. The contribution of these forces to the tertiary structure formation in designed transmembrane segments suggests that similar forces may also be a significant factor in the folding and stability of native membrane proteins.     

Interhelical spacing in liquid crystalline spermine and spermidine-DNA precipitates

The structure of polyamines-DNA precipitates was studied by x-ray diffraction. Precise measurements of the interhelix distance a(H) were obtained at different NaCl, polyamine, and DNA concentrations. Most of the results were obtained using spermine and few others using spermidine. The precipitates are liquid crystalline, either hexagonal and/or cholesteric, with an interhelical spacing that depends on the ionic concentrations and on the polyamine type. In our experimental conditions, the spacing varies from 28.15 to 33.4 angstroms. This variation is interpreted in terms of different ionic components that are present inside the precipitates and that are thought to regulate the value of the cohesive energy of DNA. These results are discussed in relation to the biological processes requiring a closeness of double helices and to the role played by polyamine analogs in cancer therapy.     

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to “breathing,” advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.     

Model for the interaction of DNA junctions and resolving enzymes.

Four-way DNA junctions are thought to be important intermediates in a number of recombination processes. Resolution of these junctions occurs by cleavage of two strands of DNA to generate two duplex molecules. The interaction between DNA junctions and resolving enzymes appears to be largely structure-specific, reflecting a molecular recognition on a significant scale. We propose a working model for this interaction that takes account of the present state of knowledge of the structure of the DNA junction, and the substrate requirements of the enzymes. We note that three different enzymes introduce cleavages at phosphodiester bonds that are presented on one side of the molecule, suggesting that the enzymes selectively interact with this face of the junction. By forcing a junction of constant sequence to adopt one or other of the two possible antiparallel isomers, we show that the junction is cleaved in such a way as to suggest a constant mode of interaction with the protein that is dependent on structure rather than sequence. We propose that the feature that is recognized is a mutual inclination of two DNA helices at approximately 120 degrees. We show that a number of DNA substrates that contain similar inclined helices, such as a three-way junction, bulged duplexes and a duplex that is curved because of repeated runs of oligoadenine sequences, are each cleaved by phage T4 endonuclease VII. This mode of DNA-protein interaction could be significant in either recombination or DNA repair processes.     

Preferential hydration of DNA: the magnitude and distance dependence of alcohol and polyol interactions

The physical forces that underlie the exclusion of solutes from macromolecular surfaces can be probed in a similar way as the measurement of forces between macromolecules in condensed arrays using the osmotic stress technique and x-ray scattering. We report here the dependence of alcohol exclusion or, equivalently, the preferential hydration of DNA on the spacing between helices in condensed arrays. The actual forces describing exclusion are quite different from the commonly assumed steric crowding coupled with weak binding. For a set of 12 nonpolar alcohols, exclusion is due to repulsive hydration interactions with the charged DNA surface. Exclusion amplitudes do not depend simply on size, but rather on the balance between alkyl carbons and hydroxyl oxygens. Polyols are included at very close spacings. The distance dependence of polyol inclusion, however, is quite different from nonpolar alcohol exclusion, suggesting the underlying mechanism of interaction is different.     

The impact of individual perceptual and cognitive factors on collective states in a data-driven fish school model

In moving animal groups, social interactions play a key role in the ability of individuals to achieve coordinated motion. However, a large number of environmental and cognitive factors are able to modulate the expression of these interactions and the characteristics of the collective movements that result from these interactions. Here, we use a data-driven fish school model to quantitatively investigate the impact of perceptual and cognitive factors on coordination and collective swimming patterns. The model describes the interactions involved in the coordination of burst-and-coast swimming in groups of Hemigrammus rhodostomus. We perform a comprehensive investigation of the respective impacts of two interactions strategies between fish based on the selection of the most or the two most influential neighbors, of the range and intensity of social interactions, of the intensity of individual random behavioral fluctuations, and of the group size, on the ability of groups of fish to coordinate their movements. We find that fish are able to coordinate their movements when they interact with their most or two most influential neighbors, provided that a minimal level of attraction between fish exist to maintain group cohesion. A minimal level of alignment is also required to allow the formation of schooling and milling. However, increasing the strength of social interactions does not necessarily enhance group cohesion and coordination. When attraction and alignment strengths are too high, or when the heading random fluctuations are too large, schooling and milling can no longer be maintained and the school switches to a swarming phase. Increasing the interaction range between fish has a similar impact on collective dynamics as increasing the strengths of attraction and alignment. Finally, we find that coordination and schooling occurs for a wider range of attraction and alignment strength in small group sizes.     

Structural and Functional Studies of the Phage Sf6 Terminase Small Subunit Reveal a DNA-Spooling Device Facilitated by Structural Plasticity

In many DNA viruses, genome packaging is initiated by the small subunit of the packaging terminase, which specifically binds to the packaging signal on viral DNA and directs assembly of the terminase holoenzyme. We have experimentally mapped the DNA-interacting region on Shigella virus Sf6 terminase small subunit gp1, which occupies extended surface areas encircling the gp1 octamer, indicating that DNA wraps around gp1 through extensive contacts. High‐resolution structures reveal large-scale motions of the gp1 DNA-binding domain mediated by the curved helix formed by residues 54–81 and an intermolecular salt bridge formed by residues Arg67 and Glu73, indicating remarkable structural plasticity underlying multivalent, pleomorphic gp1:DNA interactions. These results provide spatial restraints for protein:DNA interactions, which enable construction of a three-dimensional pseudo-atomic model for a DNA-packaging initiation complex assembled from the terminase small subunit and the packaging region on viral DNA. Our results suggest that gp1 functions as a DNA-spooling device, which may transform DNA into a specific architecture appropriate for interaction with and cleavage by the terminase large subunit prior to DNA translocation into viral procapsid. This may represent a common mechanism for the initiation step of DNA packaging in tailed double‐stranded DNA bacterial viruses.     

Cysteine-cysteine contact preference leads to target-focusing in protein folding

We perform a statistical analysis of amino-acid contacts to investigate possible preferences of amino-acid interactions. We include in the analysis only tertiary contacts, because they are less constrained--compared to secondary contacts--by proteins' backbone rigidity. Using proteins from the protein data bank, our analysis reveals an unusually high frequency of cysteine pairings relative to that expected from random. To elucidate the possible effects of cysteine interactions in folding, we perform molecular simulations on three cysteine-rich proteins. In particular, we investigate the difference in folding dynamics between a Gō-like model (where attraction only occurs between amino acids forming a native contact) and a variant model (where attraction between any two cysteines is introduced to mimic the formation/dissociation of native/nonnative disulfide bonds). We find that when attraction among cysteines is nonspecific and comparable to a solvent-averaged interaction, they produce a target-focusing effect that expedites folding of cysteine-rich proteins as a result of a reduction of conformational search space. In addition, the target-focusing effect also helps reduce glassiness by lowering activation energy barriers and kinetic frustration in the system. The concept of target-focusing also provides a qualitative understanding of a correlation between the rates of protein folding and parameters such as contact order and total contact distance.     

Symmetry laws for interaction between helical macromolecules.

The power of symmetry laws is applied in many scientific areas from elementary particle physics to structural biology. The structures of many biological helices, including DNA, were resolved with the use of pertinent symmetry constraints. It was not recognized, however, that similar constraints determine cardinal features of helix-helix interactions vital for many recognition and assembly reactions in living cells. We now formulate such symmetry-determined interaction laws and apply them to explain DNA "over-winding" from 10.5 base pairs per turn in solution to 10 in hydrated fibers, counterion specificity in DNA condensation, and forces observed over the last 15 A of separation between DNA, collagen, and four-stranded guanosine helices.     

Interaction between inclusions embedded in membranes.

We calculate the membrane-induced interaction between inclusions, in terms of the membrane stretching and bending moduli and the spontaneous curvature. We find that the membrane-induced interaction between inclusions varies nonmonotonically as a function of the inclusion spacing. The location of the energy minimum depends on the spontaneous curvature and the membrane perturbation decay length, where the latter is set by the membrane moduli. The membrane perturbation energy increases with the inclusion radius. The Ornstein-Zernike theory, with the Percus-Yevick closure, is used to calculate the radial distribution function of inclusions. We find that when the spontaneous curvature is zero, the interaction between inclusions due to the membrane deformation is qualitatively similar to the hard-core interaction. However, in the case of finite spontaneous curvature, the effective interaction is dramatically modified.